// Meta-Manifold Prover for Gowin GW1NR-9 / Tang Nano 9K // Target: 8640 LUTs, 0 DSP slices, 27 MHz // Implements: Mass Number gates, Torus topology, Menger sponge, Fold energy module MetaManifoldProver #( parameter DATA_WIDTH = 32, // Q16_16 needs 32 bits parameter ADDR_WIDTH = 16, parameter TORUS_DIMS = 5, parameter TORUS_SIZE = 8 )( input wire clk, input wire rst_n, // Control interface input wire start, output reg busy, output reg done, // Operation select input wire [2:0] op_select, // 000: MassLe, 001: TorusDist, 010: MengerHash, 011: FoldEnergy, 100: SurfaceCheck // Mass Number gate inputs (Q16_16) input wire signed [DATA_WIDTH-1:0] admissible, input wire signed [DATA_WIDTH-1:0] residual, input wire signed [DATA_WIDTH-1:0] epsilon, input wire signed [DATA_WIDTH-1:0] threshold, output reg mass_le_result, // Torus topology inputs input wire [TORUS_DIMS*4-1:0] coord1, // 4 bits per dimension input wire [TORUS_DIMS*4-1:0] coord2, output reg [11:0] torus_distance, // Menger sponge inputs input wire [ADDR_WIDTH-1:0] menger_x, input wire [ADDR_WIDTH-1:0] menger_y, input wire [ADDR_WIDTH-1:0] menger_z, input wire [DATA_WIDTH-1:0] hausdorff_dim, // Q16_16 fixed-point output reg [ADDR_WIDTH-1:0] menger_address, // Fold energy inputs (Q16_16) input wire signed [DATA_WIDTH-1:0] torus_energy, input wire signed [DATA_WIDTH-1:0] menger_energy, input wire signed [DATA_WIDTH-1:0] horn_energy, input wire signed [DATA_WIDTH-1:0] alpha, input wire signed [DATA_WIDTH-1:0] beta, input wire signed [DATA_WIDTH-1:0] gamma, output reg signed [DATA_WIDTH-1:0] fold_energy_total, // Surface translation inputs (Q16_16) input wire signed [DATA_WIDTH-1:0] surface_height, input wire signed [DATA_WIDTH-1:0] surface_ridge, output reg surface_admissible ); // State machine reg [2:0] state; localparam IDLE = 3'd0; localparam MASS_LE = 3'd1; localparam TORUS_DIST = 3'd2; localparam MENG_HASH = 3'd3; localparam FOLD_ENERGY = 3'd4; localparam SURFACE_CHECK = 3'd5; // Fixed-point multiplication (no DSP slices, use shift-add) function signed [31:0] q16_mul; input signed [15:0] a; input signed [15:0] b; reg signed [31:0] product; begin product = a * b; q16_mul = product >>> 16; // Q16.16 multiplication end endfunction // Fixed-point comparison function q16_le; input signed [15:0] a; input signed [15:0] b; begin q16_le = (a <= b); end endfunction // Mass Number gate: A <= tau * (R + epsilon) reg signed [31:0] residual_plus_epsilon; reg signed [63:0] threshold_times_residual; reg signed [31:0] threshold_times_residual_q16; // Torus distance calculation reg [3:0] dim1 [0:TORUS_DIMS-1]; reg [3:0] dim2 [0:TORUS_DIMS-1]; reg [11:0] dim_diff [0:TORUS_DIMS-1]; reg [11:0] dim_wrapped [0:TORUS_DIMS-1]; reg [11:0] dim_min [0:TORUS_DIMS-1]; integer i; // Menger hash: x ^ (y << 1) ^ (z << 2) reg [ADDR_WIDTH-1:0] y_shifted; reg [ADDR_WIDTH-1:0] z_shifted; reg [ADDR_WIDTH-1:0] hash_result; reg [ADDR_WIDTH-1:0] sum_xyz; reg [63:0] dim_times_sum; reg [ADDR_WIDTH-1:0] fractal_offset; // Fold energy weighted sum reg signed [63:0] torus_weighted; reg signed [63:0] menger_weighted; reg signed [63:0] horn_weighted; reg signed [63:0] fold_sum; // Surface check reg surface_condition; always @(posedge clk or negedge rst_n) begin if (!rst_n) begin state <= IDLE; busy <= 1'b0; done <= 1'b0; mass_le_result <= 1'b0; torus_distance <= 12'd0; menger_address <= 16'd0; fold_energy_total <= 16'd0; surface_admissible <= 1'b0; end else begin case (state) IDLE: begin if (start) begin busy <= 1'b1; done <= 1'b0; case (op_select) 3'd0: state <= MASS_LE; 3'd1: state <= TORUS_DIST; 3'd2: state <= MENG_HASH; 3'd3: state <= FOLD_ENERGY; 3'd4: state <= SURFACE_CHECK; default: state <= IDLE; endcase end else begin busy <= 1'b0; end end MASS_LE: begin // Calculate R + epsilon residual_plus_epsilon <= residual + epsilon; // Calculate tau * (R + epsilon) threshold_times_residual <= q16_mul(threshold, residual_plus_epsilon); threshold_times_residual_q16 <= threshold_times_residual[31:16]; // Check A <= tau * (R + epsilon) mass_le_result <= q16_le(admissible, threshold_times_residual_q16); state <= IDLE; done <= 1'b1; busy <= 1'b0; end TORUS_DIST: begin // Calculate Manhattan distance with wraparound (combinational) // dim1[0] = coord1[3:0], dim1[1] = coord1[7:4], etc. dim1[0] = coord1[3:0]; dim1[1] = coord1[7:4]; dim1[2] = coord1[11:8]; dim1[3] = coord1[15:12]; dim1[4] = coord1[19:16]; dim2[0] = coord2[3:0]; dim2[1] = coord2[7:4]; dim2[2] = coord2[11:8]; dim2[3] = coord2[15:12]; dim2[4] = coord2[19:16]; // Calculate distance for each dimension dim_diff[0] = (dim1[0] >= dim2[0]) ? (dim1[0] - dim2[0]) : (dim2[0] - dim1[0]); dim_diff[1] = (dim1[1] >= dim2[1]) ? (dim1[1] - dim2[1]) : (dim2[1] - dim1[1]); dim_diff[2] = (dim1[2] >= dim2[2]) ? (dim1[2] - dim2[2]) : (dim2[2] - dim1[2]); dim_diff[3] = (dim1[3] >= dim2[3]) ? (dim1[3] - dim2[3]) : (dim2[3] - dim1[3]); dim_diff[4] = (dim1[4] >= dim2[4]) ? (dim1[4] - dim2[4]) : (dim2[4] - dim1[4]); dim_wrapped[0] = TORUS_SIZE - dim_diff[0]; dim_wrapped[1] = TORUS_SIZE - dim_diff[1]; dim_wrapped[2] = TORUS_SIZE - dim_diff[2]; dim_wrapped[3] = TORUS_SIZE - dim_diff[3]; dim_wrapped[4] = TORUS_SIZE - dim_diff[4]; dim_min[0] = (dim_diff[0] < dim_wrapped[0]) ? dim_diff[0] : dim_wrapped[0]; dim_min[1] = (dim_diff[1] < dim_wrapped[1]) ? dim_diff[1] : dim_wrapped[1]; dim_min[2] = (dim_diff[2] < dim_wrapped[2]) ? dim_diff[2] : dim_wrapped[2]; dim_min[3] = (dim_diff[3] < dim_wrapped[3]) ? dim_diff[3] : dim_wrapped[3]; dim_min[4] = (dim_diff[4] < dim_wrapped[4]) ? dim_diff[4] : dim_wrapped[4]; torus_distance = dim_min[0] + dim_min[1] + dim_min[2] + dim_min[3] + dim_min[4]; state <= IDLE; done <= 1'b1; busy <= 1'b0; end MENG_HASH: begin // Calculate hash: x ^ (y << 1) ^ (z << 2) (combinational) y_shifted = menger_y << 1; z_shifted = menger_z << 2; hash_result = menger_x ^ y_shifted ^ z_shifted; // Calculate fractal offset: (x + y + z) * d_H / 65536 sum_xyz = menger_x + menger_y + menger_z; dim_times_sum = q16_mul(hausdorff_dim, sum_xyz[15:0]); fractal_offset = dim_times_sum[31:16]; // Final address: hash ^ offset menger_address = hash_result ^ fractal_offset; state <= IDLE; done <= 1'b1; busy <= 1'b0; end FOLD_ENERGY: begin // Calculate weighted sum: alpha*E_torus + beta*E_menger + gamma*E_horn (combinational) torus_weighted = q16_mul(alpha, torus_energy); menger_weighted = q16_mul(beta, menger_energy); horn_weighted = q16_mul(gamma, horn_energy); fold_sum = torus_weighted + menger_weighted + horn_weighted; fold_energy_total = fold_sum[31:16]; state <= IDLE; done <= 1'b1; busy <= 1'b0; end SURFACE_CHECK: begin // Check if surface is admissible: height >= ridge (combinational) surface_condition = q16_le(surface_ridge, surface_height); surface_admissible = surface_condition; state <= IDLE; done <= 1'b1; busy <= 1'b0; end default: begin state <= IDLE; busy <= 1'b0; end endcase end end endmodule